Method of forming a fire resistant structural beam

ABSTRACT

A method, and the resultant apparatus, for designing a fire resistant structural beam, such as a computer-aided design of a fabricated steel beam having an intumescent coating material, by obtaining a number of values for a number of physical parameters of the structural beam, including reading temperature information that comprise empirical information derived from heating a structural beam and a number of temperatures at a number of locations.

FIELD OF THE DISCLOSURE

This invention relates to a method of designing a structural beam, suchas a fabricated steel beam, and to a structural beam designed by themethod. The invention particularly but not exclusively relates tofabricated steel beams for composite or non-composite structures ofconcrete and steel.

BACKGROUND

It is known that the strength of steel starts to fall when thetemperature of the steel exceeds 500° C. or so, and falls to zero atabout 1000° C. or so. As building fires may exceed these temperatures,it is clearly desirable that structural beams made of steel retainsufficient strength to avoid deformation for a period which issufficiently long for, for example, the building to be evacuated.Typical fire protection periods for structural beams, particularly floorsupporting beams, vary from 30 to 120 minutes. The fire resistantqualities of the beam can be increased by increasing the physicalcharacteristics, that is the physical dimensions, of the beam and/or byinsulating the beam such that in the event of a fire, the rate oftemperature rise of the beam will be reduced to provide the requiredlength of fire resistance. It is known, for example, to provide asuitable fire resistant cladding, which is built around the beam onsite. This however actually requires additional on-site work, which mayextend the time required to commission a building, with attendantfinancial cost.

It is also known to apply a fire protection material to a beam, which issubject to an intumescent reaction when heated or in the presence offire. When heated, the material undergoes an interaction between itscomponents which causes the material to form a char, the thickness ofwhich is up to 50 times that of the original coating of the fireprotection material. The char has insulating properties and so decreasesthe rate of temperature rise in the steel element to which it isapplied. Hence, a structural beam may be supplied with desired fireresistant values without necessarily having to increase the physicaldimensions of the beam.

Typically, intumescent fire protection material is applied as a coatingto a structural beam by being supplied as a spray. The resulting coatinghas a thickness typically in the range of 250 to 2200 microns, andthicker if need be. The spray may be applied on site or off site. Theadvantage of applying the coating off site is that a fully finishedstructural beam is supplied to the construction site which reduces thework required on site, and hence shortens the construction period andreduces the cost.

Conventionally, when assessing the thickness of fire protection materialrequired, an engineer will consult an appropriate reference book, suchas “Fire Protection for Structural Steel in Buildings” published by theAssociation of Specialist Fire Protection and the Steel ConstructionInstitute. This will suggest an appropriate thickness of intumescentcoating to be applied to a beam depending on the section factor of thebeam, that is its perimeter distance divided by its area, and the lengthof time for which fire resistance is required.

There are difficulties in this approach in that it does not fully takeaccount of cellular beams or other structural beams provided withapertures, and it does not consider parameters such as cell spacing orweb slenderness ratio.

SUMMARY OF THE DISCLOSURE

An aim of the present disclosure is to reduce or overcome one or more ofthe above problems. In this specification, although “beams” and“structural beams” are referred to, it will be apparent that theinvention may be used with any appropriate structural component.

According to a first aspect of the disclosure, a method of designing afire resistant structural beam is provided, comprising obtaining aplurality of values for a plurality of physical parameters of thestructural beam, reading temperature information, performing an analysisstep to calculate a property of the structural beam in accordance withthe temperature information, and generating an output in accordance withthe analysis step.

The temperature information may comprise empirical information derivedfrom heating a structural beam.

The temperature information may comprise a plurality of temperatures ata plurality of locations, and where the temperature information for aposition disposed between two or more of said locations is calculated byinterpolating the temperatures at the two or more locations.

The analysis step may comprise performing calculations at a plurality ofspaced locations along the structural beam.

The spaced locations may comprise sections through the structural beam.

The spaced locations may be equidistant along the length of saidstructural beam.

The structural beam may comprise one or more apertures and the step ofobtaining a plurality of values for a plurality of physical parametersof the structural beam comprises obtaining aperture informationcomprising the location and size of the or each aperture.

The step of reading the temperature information may comprise readingmodifying factor information in accordance with the aperture informationand modifying the temperature information in accordance with themodifying factor information.

The modifying factor information may comprise a plurality of factors ata plurality of locations and the step of modifying the temperatureinformation in accordance with the modifying factor informationcomprising multiplying the temperature information by the modifyingfactor information.

The plurality of factors may be in the range 1.05 to 1.5.

The temperature information may comprise empirical information derivedfrom heating a structural beam comprising a plain beam and wherein themodifying factor information comprises empirical information derivedfrom heating a structural beam provided with one or more apertures.

The analysis step may further comprise performing additionalcalculations in the vicinity of the aperture.

The additional calculations may comprise calculating one or more of; theshear resistance of the structural beam, the bending resistance of thestructural beam, Vierendeel bending resistance, web buckling.

The method may comprise the step of calculating the required thicknessof intumescent coating to avoid failure of the structural beam with aselected period of time, the fire resistance time.

The method may comprise the step of identifying a failure mode of thestructural beam and calculating the thickness of intumescent coatingrequired to avoid the failure mode.

The method may comprise the step of identifying the location where saidfailure mode occurs and calculating the required thickness at thatlocation.

The method may comprise the step of performing said further step for aplain beam and then performing the additional calculations in accordancewith the required thickness.

The output step may comprise comparing one or more values of said one ormore properties with a predetermined criterion and generating an outputaccordingly.

The method may comprise the step of performing said analysis step forthe structural beam in the cold condition.

The method may comprise the step of modifying the values for a pluralityof physical parameters of the structural beam in accordance with theoutput and performing the method in accordance with the modified values.

According to a second aspect of the disclosure, a computer program forperforming the above method is provided.

According to a third aspect of the disclosure, a structural beam wheredesigned by a method according to a first aspect of the disclosure isprovided.

Thus, in accordance with this disclosure, is provided a fabricated steelbeam, which may be for composite steel structures with metal deckfloors, comprising lower and upper flanges and web produced from steelplate. A coating, of intumescent material, is applied of a thicknesscalculated on the basis of failure mechanism of at least one of theindividual components of the beam. The development of understanding ofthese failure mechanisms is supported by fire tests.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure will now be described by way of example only withreference to the accompanying drawings where;

FIG. 1 is a section through a hot-rolled beam of known type,

FIG. 2 is a section through a fabricated structural beam,

FIG. 3 is a side view of the structural beam of FIG. 2,

FIG. 4 is a flow chart illustrating a method embodying the presentdisclosure,

FIG. 5 a is a flow chart of a first stage of a method of designing abeam,

FIG. 5 b is a flow chart of a second stage of a method of designing abeam, and

FIG. 5 c is a flow chart of a third stage of a method of designing astructural beam,

FIG. 6 is an illustration of an arrangement of a test of a beam,

FIG. 7 is a graph showing deflection of tested beams,

FIG. 8 is a photograph of a shear failure in a tested beam,

FIG. 9 is a photograph of deformation of a tested beam,

FIG. 10 is a photograph of bending failure of a tested beam,

FIG. 11 is a division of a cross section of a beam into elements,

FIG. 12 illustrates a Vierendeel bending model,

FIG. 13 is a graph showing the rise in steel temperature of a structuralbeam provided with an intumescent coating,

FIG. 14 is a graph showing the variation of effective thermalconductivity of an intumescent coating and steel temperature,

FIG. 15 is a graph showing comparison between measured and predictedtemperatures in a first beam test,

FIG. 16 is a graph showing comparison of measured and predictedtemperatures in a second beam test, and

FIG. 17 is a graph showing a comparison of measured and predictedtemperatures in a third beam test.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to FIG. 1, a hot rolled structural beam is generally shownat 10 comprising an upper flange 11 and a lower flange 12 connected by aweb 13. The beam 10 supports a concrete floor slab shown at 14 inconventional manner. The width of the lower flange is given as B_(f),the lower flange thickness as T_(f), the web thickness as t_(w), the webheight as d, and the internal width of the upper and lower flange asb_(f). Conventionally, for a hot-rolled beam, the thickness of therequired fire protection coating is calculated on the basis of thesection factor of the whole beam, that is the ratio of the heatedperimeter to the total cross sectional area of the beam. For the beamshown in FIG. 1 this is calculated as;

$\frac{H_{p}}{A} = \frac{{4T_{f}} + {4b_{f}} + {2d} + {2B_{f}}}{{t_{w}d} + {2B_{f}T_{f}}}$

Where a beam has a small section factor, in general a low coatingthickness is required since the structural beam itself containssufficient material to withstand a relatively long period of heating,whereas a low section factor indicates that the beam will heat uprelatively quickly when exposed to a source of heat and thus fail morequickly, requiring a higher coating thickness.

As discussed hereinbefore, this method of calculating the requiredthickness of intumescent coating is not suitable for beams provided withapertures, and may also not be suitable for fabricated beams whichprovide a great deal of flexibility in providing beams with differingsizes of upper and lower apertures and web. As shown in FIGS. 2 and 3, afabricated structural beam is shown comprising an upper flange 21, alower flange 22 and a web 23 in which a plurality of apertures 24 areprovided. The structural beam 20 supports a floor slab 25. Thestructural beam 20 is further provided with a coating 26 of anappropriate intumescent material. Such a structural beam 20 is generallyreferred to as a fabricated beam or girder.

Conventionally, where a structural beam is provided with apertures 24, aguide used by engineers is that the intumescent coating 26 may becalculated from that required by a plain beam such as that shown in FIG.1, with the thickness increased by 20%. However, unexpectedly, thisthickness of coating may not be sufficient for providing the desiredfire protection, as tests of fabricated beams, both plain and providedwith apertures, show that modes of failure including bending and shearbuckling occur. In particular, the web post is particularly important,and failure mode is strongly influenced by the web slenderness ratio andcell spacing.

The method of designing a structure of the present disclosure thereforeuses empirical temperature information from fire tests of beams to findthe temperature distribution of a heated beam and perform an analysis ofone or more properties of the structural beam in accordance with thetemperature information.

The method may also use standard codes in the analysis such as BS 5950Part 8 or corresponding Eurocodes.

The method is discussed with reference to FIG. 4. At step 30, the beamparameters, that is the physical dimensions of the beams including thesize and location of any apertures, and the required fire resistancetime are obtained. The beam parameters may be entered by a designer, ormay be obtained from a beam design program or otherwise. The fireresistance time in time within which the beam may not fail, and isconventionally one of 30 minutes, 60 minutes, 90 minutes or 120 minutes.

At step 31, the temperature information for a plain beam, that is a beamwithout apertures, having the same dimensions and material obtained inFIG. 30 is read. In the fire tests as discussed in more detail below,temperature data were obtained by locating thermocouples at differentpoints on a beams with plain and/or cellular webs, and thus thetemperature information comprises a plurality of temperatures at aplurality of locations after a given time has elapsed, for example 30minutes. Because the temperature information will be for a particulardistribution of points on a plain beam, to enable the properties of thebeam to be calculated at points between these locations at 31, wherenecessary, an interpolation is performed for points between thelocations and associated temperatures to calculate the temperaturedistribution across the beam where required. Advantageously, it has beenfound that the interpolation may be a simple linear interpolation, whichis computationally simple and thus quick to perform. In a preferredimplementation, the temperature information comprises temperatureinformation derived from the experimental data by performing the linearinterpolation step. Thus, in performing the method the temperatureinformation may be used without requiring further interpolation.

In the present example, for each beam size sets of temperatureinformation at 30 minutes, 60 minutes, 90 minutes and 120 minutes areprovided, and the appropriate set is read depending on the selected fireresistance time.

At step 32, an analysis is performed to calculate the properties of thebeam at one or more locations and at each location, at the temperatureread in step 31. The properties of the beam may comprise such checks asvertical shear checks, interaction of vertical shear and bending moment,a check for lateral or torsional buckling, a concrete longitudinal shearcheck, under normal condition, and, in its construction position, theinteraction of vertical shear and bending moment and lateral torsionalbuckling. The calculations may generally be those used for a structuralbeam in the “cold”, i.e. unheated condition but using a suitable valuefor the strength of the steel at the elevated temperature. Thesecalculations are set out in our prior International patent applicationno. PCT/GB00/01324, the contents of which are incorporated herein byreference. It will be apparent that any other analysis or calculation ofother properties to be performed as desired. Advantageously, theanalysis may be performed at a plurality of longitudinally spacedlocations along the beam, and in particular where each locationcomprises a section through the beam, preferably transverse to thelongitudinal axis, as set our in our prior application. The location orsection of the structural beam with the poorest physical properties, isidentified, that is the likely failure mode of the beam, and at step 33,the required thickness of intumescent material necessary to protect thatsection of the beam is calculated, such that the temperature rise ofthat section of the beam to its failure condition is delayed for thefire resistance time entered at step 30. From the required thickness ofthe char, the thickness of intumescent material to be applied to thebeam can be calculated, and is hereinafter referred to as the requiredcoating thickness.

At step 34, where the beam 22 is provided with apertures 24, it isnecessary to further check the beam in the vicinity of the apertures. Atstep 34, modifying factor information is read for locations around andin the vicinity of apertures of a beam. In the present example, sets ofmodifying factor information are provided for apertures of differenttypes, for example for apertures having round, rectangular or “obround”shapes, and different cell spacings. Modifying factors are stored forlocations around and in the vicinity of the aperture. The modifyingfactor information is thus read from the appropriate set relating to theaperture. From the fire tests as discussed below, it has been found thatthe temperature around an aperture in a structural beam is higher thatin a similar location for a plain beam having otherwise the samedimensions, seemingly because of the smaller amount of steel availableto be heated and to sink heat away from the heated regions, and alsopotentially because of the greater perimeter area of the beam, althoughother factors may of course be relevant. Thus, the modifying factorinformation comprises a plurality of modifying factors associated with aplurality of locations. As in step 31, where necessary a linear or otherinterpolation may be performed between locations to provide modifyingfactors for required points on a beam, although in the preferredimplementation the interpolation is performed when establishing themodifying factor information from the experimental data such that nofurther interpolation is required. The modifying factors aredimensionless numbers, and empirically may be derived from measuring thetemperature at corresponding points on a beam provided with aperturesand a plain beam and calculating the ratio of the temperatures. In thepresent invention, it has been found that the modifying factors are ingeneral in the range 1.05 to 1.5. It will be apparent that this relativeincrease in temperature means that the presence of apertures in a beammay cause a beam to be very much weaker than would be conventionallyexpected. At step 35, the temperature information is thereforemultiplied by the modifying factor information.

At step 36, an analysis of one or more properties of the beam isperformed in the vicinity of the apertures in accordance with theincreased temperature values introduced by the modifying factor. Asdiscussed in detail below, the analysis may conclude calculatingparameters such as shear resistance of the beam at the opening and theVierendeel resistance around the aperture. At step 37, an output isgenerated in accordance with the analysis step 36. For example, theoutput may generate a unity factor for property at each location, wherea unity factor is a dimensionless number arising from the comparison ofthe value of the property with a predetermined criterion, and where avalue of less than 1 indicates that the value of the property for thatlocation of the beam is acceptable, and where a value of one or greaterindicates that the value of the property at that location isunacceptable. By generating and outputting unity factors in this way, itis thus easy for a designer to identify sections or locations of a beamwhere property is unacceptable and moderate the beam parameter and/orthe thickness of the intumescent material as required. The method ofFIG. 4 may be performed iteratively to provide a beam having the desiredphysical parameters and fire resistance time.

Advantageously, at step 37, the method may comprise the step ofgenerating a cost factor or cost index. This may be calculated from thephysical dimensions of the beam, with associated cost implications forthe quantity of steel required and manufacturing steps, and may alsoincorporate an indication of the cost of applying an intumescent coating26. For example, the maximum thickness of a coat of intumescent material26 applied in a single pass may be limited, and it may be more costeffective to slightly increase the physical dimensions of a beam ratherthan performing to two or more spring steps to build up a requiredthickness of a coating 26. This assists in avoiding un-economicaldesigns, such as those including relatively small thin structural beamswith an excessively thick intumescent coating 26.

The method according to the invention thus permits a suitable design ofbeam to be arrived at, taking into account behavior of the web post,based on experimental data from tested beams.

Advantageously, the method of FIG. 4 may treat the flanges 21, 22 andweb 23 of the beam 20 independently. That is the temperature rise may becalculated for each part or “element” of the beam assuming a differentchar thickness and different thickness of intumescent coating for eachpart, taking into account the failure mechanism of each element. Thedetermining factor for the thickness of intumescent coating at 26 canthen be one of

1. Three coating thickness. Applying appropriate thickness to eachindividual element to prevent the mechanism likely to lead to structuralfailure for that element (within the fire resistance time required) or

2. Single coating thickness. By applying the highest coating thicknessrequired by a single element to prevent failure (within the fireresistance time required) to all three elements or

3. Two coating thickness. By applying the coating thickness required toprevent mechanism likely to lead to structural failure for the worstcase flange (within the fire resistance time required) to both flanges.Then to apply a different coating thickness similarly required for theweb to prevent the mechanism likely to lead to structural failure(within the fire resistance time required).

The invention may incorporate stiffening elements in and around serviceholes in the web to prevent or delay certain types of disadvantageousfailure mechanisms such as Virendeel bending or catastrophic shear.These stiffeners may be horizontal or vertical plate stiffeners,generally to be welded in place around apertures. In some cases, acircular aperture provided in the web of the beam may requirestrengthening in the fire condition. In such an eventuality a shortlength of circular hollow section (CHS) may provide the strengthening ofappropriate outside diameter and wall thickness. The CHS should beplaced inside the hole and the outside diameter should be sufficient toprovide a close fit to the hole to allow the hollow section to be weldedin place. Alternatively the circular stiffener may be formed from platerolled to shape.

Advantageously, the method such as the embodiment illustrated in FIG. 4may be incorporated in a general method of designing a beam such as thatdescribed in our earlier application. In an earlier application, astructural beam may be designed in the cold condition taking intoaccount all loads etc., and then the fire resistance of the structuralbeam is performed by performing the same calculations, at the samelocations if appropriate, at the higher temperature found in thetemperature information.

Referring now to FIGS. 5 a to 5 c, the various steps of the methodaccording to this invention are shown as a flow chart. The method may bebroken down into three stages, a first, input stage as shown in FIG. 5a, an analysis stage shown in FIG. 5 b and an output stage shown in FIG.5 c. In the present example, the method is envisaged as being performedby a computer program and designer.

In the input stage of the method, the relevant parameters of the beamand the load and application of the beam are entered. In step 1.1 a beamtype may be selected from a library of predefined beam types, oralternatively a customised beam type may be provided by the designer.

In steps 1.2 to 1.5, data on the beam size and load is provided. In step1.2, it is specified the beam is a floor or roof beam, whether the beamis to be an internal beam or an edge beam, the distance to be spanned bythe beam and the distance to adjacent beams on each side. The profile ofthe deck to be supported by the beam is then provided. Again, theprofile may be selected from a library of predefined profiles or theparameters for a preferred profile may be provided. The floor plan isthen entered including the orientation of the deck, the location andnumber of secondary beams and beam restraint details. Details of theconcrete slab to be supported by the beam are then entered, includingthe depth of the slab, the type and grade of the components of the slaband of the reinforcement mesh provided in the slab.

At steps 1.6 and 1.7, the details of the load to be borne by thebuilding are entered, including imposed, service and wind loading, anypartial safety factors and the limits of the natural frequency anddeflection of the structure.

In step 1.7, any load additional to those imposed by the floor plan andloading details are entered, both point loads and uniformly distributedloads. This input can be confirmed by displaying a configuration of atypical bay.

If shear connectors are to be used, the number and spacing are enteredin step 1.8.

In steps 1.9, 1.10 and 1.11, parameters of the beam are provided, inparticular, the top and bottom flange dimensions, the web depth andthickness and details of any change point in the beam, together with thenumber, spacing and size of any apertures in the web and the provisionof any beam stiffeners.

At step 1.12, the required fire resistance time is enteredconventionally selected from 30 minutes, 60 minutes, 90 minutes or 120minutes, and partial safety factors for the fire limit applied.

The input stage thus allows the designer to provide the details of thebeam shape, web openings, web stiffeners, beam geometry between changepoints and other parameters as desired. Such parameters may be selectedfrom a library of predetermined shapes or parameters, or where themethod is implemented on a computer program, may be determined by saidprogram.

It may be envisaged, that where the method is implemented on a computerprogram or otherwise, suitable graphical displays may be provided toconfirm the parameters entered.

Once the desired values for these parameters have been provided, theanalysis stage is then performed.

Referring now to FIG. 5 b, the analysis stage asks for furtherinformation as to whether the beam is composite or not and whether it isto be propped or not, and the steel grade. Checks for three calculationconditions are then performed in steps 2.2, 2.3 and 2.4 in FIG. 3.

Step 2.2 is the so-called “normal condition” where checks are made onthe properties of the beam in situ in a finished building i.e. when thestructure of which the beam is to form a part is complete. The ultimatelimit calculations are performed for a plurality of properties at eachof a plurality of discrete locations, in the present example 51 discretesections through the beam disposed longitudinally spaced along thelength of the beam. The sections may be equidistant from one another ormay be spaced otherwise as necessary. In step 2.2, the applied load isfirst calculated and then four main properties calculated;

-   -   1) the vertical shear force on the beam and the bending moment,    -   2) the interaction of the bending moment and vertical shear,    -   3) the lateral torsional buckling of the beam, and    -   4) the concrete longitudinal shear resistance.

Further properties which may be calculated include any necessarytransverse reinforcement, and the weld throat thickness.

The calculated values are compared to a predetermined criterion and aunity value calculated for the discrete section having the leastacceptable calculated value of that property.

A unity value for a given property is a unitless value indicatingwhether the calculated value for a given property meets thepredetermined criterion. If the unity value is greater than 1, thisindicates a failure mode i.e. the calculated value fails to meet thepredetermined criterion. A value of 1 shows that the value of theproperty exactly meets the predetermined criteria, and of less than 1shows that the value of the property is more than sufficient to meet thecriteria. In practice, optimisation of the design requires that eachunity value be less than but approaching 1. The unity value may becalculated by calculating the ratio of the calculated value with actualforces in the element.

Where the beam comprises adjacent sections having differing tapers,properties relating to the stability of the web and flange at or near ajunction between two such sections is calculated. The propertiescomprise:

-   -   1) the maximum change angle, i.e. the maximum difference in the        angle of taper between the two sections,    -   2) the web buckling resistance, and    -   3) the web bearing resistance.        For the web buckling resistance and the web bearing resistance,        the calculated value is compared to a predetermined criterion        and a unity value calculated for the discrete section having the        least acceptable calculated value of that property.

Where the web is provided with one or more apertures, furthercalculations are performed at a plurality of points, in the presentexample around the aperture.

Using the results of these calculations, a unity value for each of thefollowing properties, each representing a failure mode, is calculated;

-   -   1) modified calculation of vertical shear,    -   2) interaction of vertical shear and bending moment,    -   3) Vierendeel capacity,    -   4) web buckling capacity, and    -   5) web post horizontal shear.

In the next step 2.3 of the analysis stage, the so-called “constructioncondition” the properties of the beam are checked for the condition whenit is in situ but when no load, e.g. from a floor slab, is applied. Thefollowing properties are checked;

-   -   1) interaction of the bending moment capacity and vertical shear        capacity in the absence of the concrete slab, and    -   2) the lateral torsional buckling of the beam.

Where apertures are provided in the web, the following properties arecalculated for a section through the centerline of the or each apertureas in step 2.2 above;

-   -   1) modified calculation of vertical shear,    -   2) interaction of vertical shear and bending moment,    -   3) Vierendeel capacity,    -   4) web buckling capacity, and    -   5) web post horizontal shear.

Again, the calculated value for each property is compared to apredetermined criterion and a unity value calculated for the discretesection having the least acceptable calculated value of that property.

In step 2.4 of the analysis stage, the “serviceability condition”, thefollowing properties are calculated.

-   -   1) concrete compressive stress    -   2) steel tensile stress    -   3) steel compressive stress    -   4) natural frequency of vibration of the beam

For each of these properties a unity value is calculated as in steps 2.2and 2.3 above.

In the serviceability condition, a check may also be made on thedeflection of the beam, The deflection checks may include, in theconstruction condition, the self weight deflection of the beam whenpropped or un-propped. In the normal condition, the deflection due toimposed loads and superimposed dead loads may be calculated on the basisof the composite beam properties, and a total deflection check beperformed. The deflection checks in the present example do not generatea unity value, but are instead compared to predetermined criteriaprovided by the designer, for example the maximum acceptable totaldeflection of the beam. In the present example, the deflection checksare optional and any or all may be selected or omitted by the designer.

At step 2.4A, a fire resistance test is performed as describedhereinbefore, using the beam parameters entered in steps 1.1 to 1.11,and an output generated.

At the display step 2.5, each property is displayed including theresults of the fire resistance test 2.4A, together with the ‘criticalvalue’ the corresponding unity value for a discrete section having theleast acceptable calculated value of that property (usually the maximumvalue), or other indication of the comparison with a correspondingcriterion, or calculated value for the property, as appropriate.

If at step 2.6 the critical values are acceptable, the designer proceedsto stage 3 of the method. Where a unity value exceeds 1 as in step 2.7,the value for that property in the relevant section is ‘critical’ andhence likely to lead to failure of the beam. The information thusdisplayed draws the designer's attention to where the beam is deficient.The designer may then revise the values of the parameters (step 2.7A)and supply the amended parameters at the input step 1.10. To vary thefire resistance of the beam the designer may modify the dimensions ofthe beam, or vary the coating thickness or modify the size of parts ofthe structural beam, or add stiffeners or any combination of these.

The designer then returns to the input stage to modify the beam detailsaccordingly.

However, when a unity factor is substantially below 1 (step 2.8), thisindicates that the beam is over-designed for the intended load. Toreduce beam weight, cost etc. it is desirable to increase the unityfactor towards 1 whilst remaining below 1, thus optimising the design.The information displayed thus permits the designer to quickly identifythose sections of the beam where the design can be optimized and revisethe beam parameters accordingly (step 2.8A). The revised beam parametervalues are entered at step 1.10.

The process of revising the beam parameters and viewing the calculatedunity factors can be performed iteratively until, at step 2.6, thecritical factors are acceptable, i.e. the unity factors are all below 1but sufficiently close thereto for the design to be sufficientlyoptimized and the method proceeds to the output stage.

At the output stage, as shown in FIG. 5 c the details are output at step3.1, for example by saving to a data file, or in any other format asdesired. When the beam parameters are output, the parameters may besupplied as a printed document, in for example a standard format, or maybe supplied as a computer data file in an appropriate format, forexample on a computer disc, or tape, or any other medium, or displayedon a screen, or in any form as desired. It might be envisaged that sucha data file could be, for example, transmitted by email to the clientand/or to the beam fabricator. At step 3.2, the process is then repeatedfor all beams for which design is required. Finally, at step 3.3 whenthe parameters for all desired beams are all specified, it might be atthis stage that a supplier may be contacted for details of the design,supply and fabrication costs of the beams, or the closest match from alibrary of predetermined beam types may be indicated and selectedaccordingly.

When an appropriate final design is arrived at, a cost may be calculatedfor a structural beam according to the design, fabrication drawingsprepared, or indeed a manufacturing apparatus be controlled to fabricatea structural beam according to the design. Such a manufacturingapparatus may for example comprise cutting means to cut sheet metal toprovide a web part and/or flange parts of desired shape, and may furthercut apertures in the web part. The manufacturing apparatus may furtheror alternatively comprise welding means to join the web part and flangeparts to form a beam. Such an apparatus is disclosed in our co-pendingapplication no. GB9926197.6. Of course, any appropriate manufacturingapparatus may be used as desired. Where the method is performed using acomputer program, the computer may be provided as part of amanufacturing means comprising said manufacturing apparatus.

The provision of a plurality of standard beam parameters in a library aspart of the program thus further accelerates the design process byproviding that some or all of the parameters of the beam need not besupplied by the designer.

The temperature information and modifying factor information ispreferably stored as computer-readable files, such that where the methodis performed by a computer program, the computer program is able to readthe required temperature information and modifying factor informationand perform the analysis accordingly without further invention from adesigner.

Any appropriate intumescent material may be used as desired. Generally,intumescent coating material may be applied in the thickness in therange 0.2 mm to 2.2 mm, although any appropriate material and thicknessmay be used depending on application process to be used and thecharacteristics of the particular intumescent coating material to beused.

Assessing Fire Resistance of Beams

The fire resistance of a fabricated steel beam is assessed by amodification to that used in normal conditions. The procedure,therefore, generally follows the step-wise approach. The main differenceis that the material properties used are those are appropriate toelevated temperatures. Reduced partial factors for material strengthsand loads appropriate for the fire limit state are taken from BS 5950-8.

The temperature of parts of the cross-section depend on the amount offire protection applied and the required fire resistance. In thisexample, the beams must be protected with the special intumescentcoating, “Firetex FB 120”, developed by W and J Leigh.

Three loaded fire resistance tests on protected composite beams werecarried out at Warrington Fire Research Center (WFRC) and numerousunloaded short sections have been tested at WFRC and W and J Leigh'stest furnace at Bolton. Based on these tests, a mathematical model ofthe performance of steel sections protected with “Firetex FB 120” hasbeen developed. Using this model, the temperature distribution on anysection may be obtained. From the temperature distribution, the reducedshear, global bending and Vierendeel bending resistance of openings maybe calculated.

An important feature of the thermal model is its ability to allow usersof the Fbeam software to optimize the design of the beam so that thethickness of protection can be applied in one coating. The maximumthickness that can be applied in one coating is approximately 1.5 mm.The software will warn users if the necessary thickness is greater thanthis maximum thickness so that the user can change the beam design, e.g.increase the web thickness. Thicknesses greater than 1.5 mm willnormally have to be applied in two coatings resulting in considerableincrease in cost of the fabricated steelwork.

The structural model used to assess the resistance to local and globalactions is described in Section 2 and the development of the thermalmodel is described in Section 3. The recommendations only apply tocomposite beams and do not apply to non-composite or tapered beams.

1. Fire Test Program

The purpose of the test program was to investigate the behavior ofcomposite fabricated beams with web openings in fire and to establishthe necessary thickness of fire protection to achieve 120 minutes fireresistance. The test program consisted of three fire protected loadedbeam fire tests at WFRC supplemented by a number of unloaded fireprotected short beams which were tested alongside the loaded beams atWFRC and in W and J Leigh's own furnace.

In the first two tests, the applied thickness of intumescent coating wasslightly greater than the 1.5 mm which can normally be applied in onecoat. However the thickness of protection in the third test was veryclose to 1.5 mm.

The main details of these tests are now summarised, as follows:

1.1 Beam Test 1

The general arrangement of the test on a fabricated steel beam withcircular openings is shown in FIG. 6. The beam details were:

Depth of steel beam 400 mm Top flange 200 mm × 15 mm Bottom Flange 200mm × 35 mm Web thickness 12 mm Steel grade* S275 Composite Slab 1200 mmwide × 120 mm deep Grade 30 concrete 51 mm deep Holorib steel deckingA193 mesh reinforcement Shear connectors 2 19 mm diameter studs @ 150centers Openings, on center of 2 × 240 mm diameter web at quarter pointsFire protection 1.84 mm FB 120 (average thickness)

Four equal point loads of 120 kN were applied to the beam. Under thisloading the critical structural condition for normal design was in theregion of the openings rather than overall bending of the beam, which isusually the controlling condition.

The beam failed after 117 minutes due to excessive deformation ofapproximately span/30. The deformations recorded in all three tests areshown in FIG. 7. The deflection increased rapidly when a shear failureoccurred at one of the openings, as illustrated in FIG. 8.

At failure, the average bottom flange temperature was 700° C. and theweb temperature remote from the opening was 715° C. The temperature ofthe web at 20 mm from the edge of the opening was 875° C.

1.2 Beam Test 2

The general arrangement of the test was similar to Beam Test 1, exceptthat the two openings were rectangular and one opening had both top andbottom stiffeners. The beam details were:

Depth of steel beam 400 mm Top flange 200 mm × 20 mm Bottom flange 200mm × 45 mm Web thickness 15 mm Steel grade S275 Composite Slab 1200 mmwide × 120 mm deep Grade 30 concrete 51 mm deep Holorib steel deckingA193 mesh reinforcement Shear connectors 2 19 mm diameter studs @ 150centers Openings, on center of 350 mm long × 200 mm high, unstiffenedweb at quarter points 450 mm long × 175 mm high, stiffened with bothsides with 50 × 6 steel plates Fire protection 2.01 mm FB 120 (averagethickness)

In order to ensure that 120 minutes fire resistance was achieved, theapplied loading was reduced to 110 kN at each point. Under this loadingthe critical structural condition for normal (cold) design was again inthe region of the openings. Rectangular openings may be expected to failin Vierendeel (local) bending due to the transfer of shear forces.

The beam failed after 135 minutes due to excessive deformation (FIG. 7).At failure both openings were beginning to show signs of Virendeelbending failure (FIG. 9).

At failure, the average bottom flange temperature was 730° C. and theweb temperature remote from the opening was 780° C. The temperature ofthe web 20 mm from the edge of the opening was 900° C.

1.3 Beam Test 3

The test was very similar to Beam Test 1, except that the two circularopenings were slightly larger and were fitted with ring stiffeners. Theclear internal diameter of the opening was the same as in the firsttest. The beam details were:

Depth of steel beam 400 mm Top flange 200 mm × 15 mm Bottom flange 200mm × 35 mm Web thickness 12 mm Steel grade S275 Composite Slab 1200 mmwide × 120 mm deep Grade 30 concrete 51 mm deep Holorib steel deckingA193 mesh reinforcement Shear connectors 2 19 mm diameter studs @ 150centers Openings, on center of 2 × 240 mm diameter ring stiffener. webat quarter points Fire protection 1.52 mm FB 120 (average thickness)

The thickness of fire protection was reduced to 1.52 mm and the pointloads were reduced to 100 kN to ensure that 120 minutes fire resistancecould be achieved. Under this loading the critical structural conditionfor normal (cold) design was again in the region of the openings.

The beam failed after 121 minutes due to excessive deformation. However,in this test there appeared to be no local deformation at the openingsand failure was by overall beam bending (FIG. 10).

At failure the average bottom flange temperature was 733° C. and the webtemperature a distance from the opening was 785° C. The ring stiffenershad the effect of the reducing the temperatures recorded close to theopenings.

1.4 Unloaded Tests

Data on the performance of the protection material was collected in 13tests on unloaded short sections and the three loaded beam tests. Thesections sizes and protection thickness for all these tests aresummarised in Table 1.

In all but one of the tests the intumescent coating performed in apredicable manner for up to and beyond 120 minutes. In test T1 A, whichhad the thinnest coating of approximately 0.6 mm, the steel temperaturerose rapidly after 85 minutes indicating that the coating had becomedetached (a stickability failure).

TABLE 1 Summary of details of all protected sections Steel thickness(mm) Protection thickness (mm) Bottom Top Bottom Top Ref Openings FlangeWeb Flange Flange Web Flange Tests at W and J Leigh 4410 None 45 15 201.17 1.27 1.27 4412 None 35 12 15 1.57 1.34 1.34 4429 Circular 35 12 151.56 1.73 1.73 4430 Rect (s) 45 15 20 1.42 1.48 1.48 4432 Rect 35 12 151.45 1.41 1.41 4433 Rect (s) 35 12 15 1.56 1.44 1.44 4447 None 35 12 151.15 1.05 1.05 4449 Rect 35 12 15 1.14 1.09 1.09 4482 None 35 12 15 1.201.09 1.09 Tests at Warrington Fire Research Center T1 2 Circular 35 1215 1.76 1.78 1.7 T1 A None 45 15 20 0.59 0.61 0.54 T2 2 Rect (s) 45 1520 1.59 1.83 1.65 T2 A None 15 10 15 1.82 1.5 1.7 T3 2 Circ (s) 35 12 151.48 1.49 1.49 T3 A None 15 10 15 1.48 1.52 1.52 T3 B None 25 10 15 1.491.52 1.52 Note: Circular refers to circular opening(s) 240 mm diameterRect refers to rectangular opening(s) T1, 2, 3 refer to loaded beamtests T1 A etc refers to unloaded short beam sections (s) refers tostiffened opening(s)2. Structural Model

The design rules are expressed in a step by step in a manner similar tothat followed for normal design. The rules have been developed by SCIand follow the principles of BS5950-8 and EC4-1-2.

2.1 Bending Resistance of Plain Beam

The bending resistance of a beam is calculated using plastic bendingtheory.

The plastic neutral axis of a composite beam may be determined byequating the compression and tensile forces in the concrete and steelelements, such that:

${{\sum\limits_{i = 1}^{n}{A_{i}p_{y,\theta,i}^{{+ l} -}}} + {\sum\limits_{i = 1}^{m}{A_{i}f_{c,\theta,i,}}}} = 0$where:

-   A_(i) is the area of element i.-   P,_(y,θ,i) is the effective yield strength of steel element i.-   f_(c,θ,i) is the design strength of concrete element i at    temperature θ. Tension in concrete is ignored.

The design moment of resistance, Mfi,t,Rd, of a composite beam may bedetermined by taking the moment of each element about the plasticneutral axis, as follows:

$M_{{fi},t,{Rd}} = {{\sum\limits_{i = 1}^{n}{A_{i}z_{i}p_{y,\theta,i}}} + {\sum\limits_{i = 1}^{m}{A_{i}z_{i}f_{c,\theta,i}}}}$where:

-   zi is the distance of element I measured to the plastic neutral    axis.

Partial shear connection is taken into account in the similar manner tothat employed for normal design. In fire, the resistance of shearconnectors is based on a temperature equal to 80% of the top flangetemperature. The compressive force in the concrete is limited by theresistance of the shear connectors from the support to the point underconsideration.

7.2.2 Shear Resistance of Plain Beam

In fire, the total shear resistance is made up of contributions from theconcrete slab, the top flange and the web. The contribution of thebottom flange to the shear resistance is generally small and is ignored.V _(overall) =V _(slab) +V _(topflange) +V _(web)Slab Contribution

The shear resistance of the solid portion (above the steel deck) of theconcrete slab is considered to act over an effective width of 3 ds,where ds is the slab depth, and is given by:

$V_{slab} = {3v_{c}k_{c} \times d_{s}d_{top} \times \left( \frac{1.5}{1.3} \right)}$where:

-   vc shear strength of lightly reinforced slab in normal conditions-   kc concrete strength reduction factor (see below)-   ds depth of composite slab-   dtop Depth of concrete above the steel deck

The ratio of 1.5:1.3 comes from the different partial factors forconcrete strength in normal and in fire conditions.

The strength reduction factor for concrete, kc, is assumed to vary withfire resistance time as follows:

TABLE 2 Effective concrete strength reduction factor Fire Effectivestrength reduction resistance (mins) factor for concrete, kc 30 1.0 600.9 90 0.8 120 0.7Top Flange Contribution:

The shear resistance of the top flange is based on the web thickness andtwo lengths of weld (assumed to be 16 mm) and is given by:V _(topflange)=0.6p _(y,θ) t _(ft)(16+t _(w))where:

-   tf is the thickness of the top flange-   tw is the web thickness-   p_(y,θ) is the reduced strength of the steel at flange temperature    θf    Web Contribution:

The shear resistance of the web is given by:V _(web)=0.6×A _(v) p _(y,θ)where:

-   Av is the shear area of the web,-   p_(y,θ) is the reduced strength of the steel at web temperature, θw

The effective web thickness for bending checks of the web-flangesections should be reduced in the presence of high shear force, asfollows:

$t_{eff} = {{{t_{w}\left\lbrack {1 - \left( {\frac{2V_{0,{fire}}}{V_{total}} - 1} \right)^{2}} \right\rbrack}\mspace{20mu}{for}\mspace{14mu}\frac{V_{0,{fire}}}{V_{total}}} \geq 0.5}$where:

-   teff is the effective web thickness-   tw is the actual web thickness-   Vtotal is the total shear resistance of the section

For low shear regions, teff=t.

2.3 Shear Resistance of Beam With an Opening

At an opening, the total shear resistance of the web is in two parts.

Web Contribution:

For an unstiffened web, the shear resistance is given by:V _(w)=0.6×(A _(v1) p _(y,θ,1) +A _(v2) p _(y,θ,2))where:

-   A_(v1) is the shear area of the upper web-   A_(v2) is the shear areas of the lower web-   p_(y,θ,1) is the effective yield strength of the upper web at    temperature θ1-   p_(y,θ,2) is the effective yield strength of the lower web at    temperature θ2    2.4 Bending Resistance

The bending resistance of the cross section at an opening is calculatedusing plastic bending theory as described in Section 2.1. The webthickness is taken as t_(eff) and any suitably welded horizontalstiffeners are included. The section is divided up into up to 9 elements(FIG. 11) and the calculation takes into account the temperature andstrength of each element. Any concrete at the level of the steel deckingis ignored.

2.5 Vierendeel Bending

The Vierendeel bending resistance of an opening is given by the sum ofthe 4 bending resistances at the corners of the opening calculated usingt_(eff). At the top of the section one of these resistances includes acontribution from the composite slab. All the other 3 resistances aredue to the steel Tee sections. The total Vierendeel bending resistanceis therefore:M _(v) =M _(vc,θ) +M _(t,θ)+2×M _(b,θ)

These bending resistances are calculated using the method given inSection 7.2.1, using the temperature dependent material strengths.

The Vierendeel bending resistance of the lower web-flange section(M_(b,θ)) is reduced by the presence of shear and tensile forces, and isgiven by:

$M_{b,\theta,{eff}} = {M_{b,\theta}\left\lbrack {1 - \frac{M_{o}}{M_{{fi},{Rd}}}} \right\rbrack}$

The Vierendeel bending resistance of the non-composite upper web-flangesection is also reduced by the presence of shear and axial force. FIG.12 Vierendeel bending model used in fire

The axial load effect is small when the section is close to the plasticneutral axis and, in fire, any reduction is ignored. Although this is aslightly unconservative approach, other conservative balancingassumptions are made. The largest of these is the beneficial effect ofthe tensile resistance of the reinforcement which is not included.

The shear effect is taken into account by limiting the depth of anunstiffened web so that the remainder can be classified as Class 2. Therule used for normal design is adopted in fire.

The Vierendeel bending resistance of the composite section above theopening is calculated assuming that only the number of shear connectorsprovided in a length (l+Ds) above the opening, where Ds is the depth ofthe slab.

The applied Vierendeel moment is V_(o,fi)l, where l is the effectivelength of the opening and V_(o,fi) is the shear force at the center ofthe opening at the fire limit state.

For equilibrium:M_(v)≧V_(o)l

As in normal design, the minimum shear force is taken as 15% of themaximum shear force at the ends of the beam in order to take account ofasymmetry of loading.

2.6 Web Buckling

The unstiffened vertical edge of an opening should be checked bybuckling as a strut, by considering a compression force of Vt actingover an effective width of web. The effective width is assumed to beequal to that taken for normal temperatures but the shear force, Vt, isthe shear force transferred by the web only above the opening.

In fire, web buckling is checked using a modified buckling curve andelevated temperature properties for effective yield strength and elasticmodulus.

3. Thermal Model

The purpose of the thermal model is to enable the temperature of variousparts of a beam to be predicted for fire resistances of 30, 60, 90 and120 minutes and for practical thicknesses of Firetex FB 120.

The fire test results were analysed using various methods. The bestcorrelation was made using a method which defines an effective thermalconductivity for the intumescent coating. This effective thermalconductivity changes during a fire resistance test and was found todepend on the coating thickness, the steel temperature and the sectionfactor (A/V) of the coated part.

The method of analysis is based on a method given Eurocode 3, Part 1.2(EC3-1-2) and in ENV13381-4. In both these codes the incremental rise intemperature of the steel is given by the differential equation:

${\Delta\;\theta_{s}} = {{\frac{\lambda_{i}/d_{i}}{C_{a}\rho_{a}}{\frac{A_{i}}{V}\left\lbrack \frac{1}{1 + {\frac{2}{3}\xi}} \right\rbrack}\left( {\theta_{t} - \theta_{s}} \right)\Delta\; t} - {\left( {{\mathbb{e}}^{\frac{\xi}{5}} - 1} \right)\Delta\;\theta_{t}}}$

-   Δθ_(s)=incremental increase in steel temperature (° C.)-   λi→=thermal conductivity of protection material (W/m° C.)-   di=thickness of protection material (m)-   C_(a)=specify heat of steel (J/kg° C.)-   C_(i)=specific heat of protection material (J/kg° C.)-   ρ_(a)=density of steel (kg/m3)-   ρ_(i)=density of protection material (kg/m3)-   Ai/V=section factor (m−1)(i.e. Hp/A)-   θt=ambient gas temperature at time t(° C.)-   θs=steel temperature at time t(° C.)-   Δt=time interval(s)-   Δθt=increase of the ambient temperature Δt(° C.)

The fire temperature, θt, is taken as the standard fire to BS 476.

During the tests the temperature of various parts of beam were recorded(FIG. 13).

A feature of the performance of an intumescent coating is it does notstart to intumesce (expand) and protect the steel until the steelreaches about 200° C. After this temperature it becomes a very effectiveinsulator and limits the rate of rise of steel temperature. Thisbehavior can be seen from the temperature response in FIG. 13.

From this temperature data, the rate of rise in temperature may bederived and hence, using the above equation, the effective thermalconductivity may also be established. For an intumescent coating, thethickness will increase as the coating intumesces. As it is verydifficult to measure the instantaneous thickness, a constant thickness,approximately equal to the maximum thickness, was assumed and wasderived. This effective value was found to vary with steel temperature,nominal coating thickness and section factor of the coated part. Atypical plot showing the variation of thermal conductivity is shown inFIG. 14.

The behavior shown in FIG. 14 can be closely approximated by an initialphase in which the steel is only very lightly insulated and two phasesin which the effective thermal conductivity is initially linearlyfalling and then linearly increasing. By analysing a number of sets oftest data and carrying out regression analyses, the variation seen inthese three phases can be expressed in terms of the section factor ofthe steel and the dry film thickness of the coating.

Separate analyses were carried out for the bottom flange, the web andthe top flange.

4. Predicted and Measured Performance in Fire

4.1 Structural Performance

For each of the loaded fire tests, the predicted performance and themeasured performance has been compared. The predicted strength of eachbeam at the end of each test has been assessed using the methodsdescribed in Section 7.2 using the measured steel temperatures. Theresults of these analyses are summarised in Table 7.3. In each case, thestructural model correctly identified the mode of failure observed inthe test. Also, the predicted load capacity of each beam was close tothe applied load in the test.

In Test 1, the mode of failure was shear at one of the openings. Thehighest Unity Factor of 0.96 indicates that shear at the openings wasidentified as the governing mode.

In Test 2, the beam was showing signs of a Vierendeel bending failure atboth openings. The highest Unity Factors of 1.00 and 1.01 indicate thatVierendeel bending at the openings was identified as the governing mode.

In Test 3, no local failures occurred and the beam was starting to failin overall bending. The highest Unity Factor of 0.94 indicates thatoverall bending was identified as the governing mode.

In Test 3, circular openings were fitted with ring stiffeners. Theeffect of ring stiffeners has not been examined in any depth so theVierendeel bending resistance, which is likely to be influenced by aring stiffener, has not been computed. However, in Test 3 the ringstiffeners had the effect of containing the intumescent coating and thusreducing web temperatures. At the time of writing, ring stiffeners arenot included in the scope of the FBEAM software for both normal and firedesign conditions.

TABLE 3 Summary of applied loads and predicted resistances. Test 1 Test2 Test 2 Test 3 Beam checks (unstiffened) (stiffened) Maximum applied260 238 217 moment Moment resistance 312 312 231 Bending unity factor0.84 0.77    0.94 Hole checks Applied shear 124 114 114 103 Total shearresistance 129 142 153 165 Shear unity factor 0.96 0.80 0.74    0.63Applied moment 195 179 179 163 Moment resistance 245 270 282 248 Bendingunity factor 0.79 0.66 0.63    0.66 Vierendeel bending 19.8 39.6 50.6resistance Applied Vierendeel 14.8 39.7 51.1 Outside moment ScopeVirendeel unity factor 0.75 1.00 1.01 Applied web load 14.5 20.6 25.1  19.4 Web buckling capacity 31.9 23.1 45.7  21 Buckling unity factor0.46 0.89 0.55    0.924.2 Thermal Performance

Comparisons between measured temperatures and predicted temperatures areshown in FIG. 15, FIG. 16 and FIG. 17. Generally, the predictedtemperatures are higher than the measured values.

4.3 Summary of Comparisons

The comparisons shown in Sections 7.4.1 and 7.4.2 show that thestructural and thermal models are adequate to predict the performance ofFabsec beams protected with Firetex FB 120. The differences betweencalculation and test are not significant. Also, in practicalapplications there are many inherently conservative factors which arenot taken into account in the modelling. Actual material properties willbe greater than the nominal properties which are used in calculationsand the average applied thickness of coating will, invariably, begreater than the specified value.

In the present specification “comprises” means “includes or consists of”and “comprising” means “including or consisting of”.

The features disclosed in the foregoing description, or the followingclaims, or the accompanying drawings, expressed in their specific formsor in terms of a means for performing the disclosed function, or amethod or process for attaining the disclosed result, as appropriate,may, separately, or in any combination of such features, be utilised forrealizing the disclosure in diverse forms thereof.

1. A method of designing a fire resistant structural beam including aplurality of apertures based on empirical temperature informationobtained from conducting fire tests on a first fabricated beam and asecond fabricated beam, the method carried out by a computer program andcomprising: obtaining a plurality of values for a plurality of physicalparameters of the fire resistant structural beam; selecting a fireresistance time for the fire resistant structural beam from a pluralityof available fire resistance times; reading temperature informationassociated with the selected fire resistance time, the temperatureinformation comprising, or derived from, a plurality of temperaturesmeasured at a plurality of locations on a first fabricated beam that issimilar to the fire resistant structural beam and wherein the pluralityof temperatures were obtained from a fire test of the first fabricatedbeam and measured after a time equal to the fire resistance time hadelapsed, reading modifying factor information associated with theselected fire resistance time, the modifying factor informationcomprising at least one modifying factor for each aperture, wherein themodifying factor is derived from empirically obtained temperaturesmeasured adjacent an aperture of a second fabricated beam that hasundergone a fire test, performing an analysis comprising: calculating afirst property of the fire resistant structural beam at one or morelocations on the fire resistant structural beam, the first property ateach location calculated as a function of one of the plurality oftemperatures of the temperature information, and calculating a secondproperty of the fire resistant structural beam at a plurality oflocations around the apertures and on the fire resistant structuralbeam, the second property at each location around the aperturescalculated as a function of one of a plurality of temperatures obtainedby multiplying the plurality of temperatures of the temperatureinformation by the modifying factor, and generating an output indicatingwhether the fire resistant structural beam is likely to fail inaccordance with the analysis step.
 2. A method according to claim 1wherein the temperature information for a position disposed between twoor more of said locations is calculated by interpolating thetemperatures at the two or more locations.
 3. A method according toclaim wherein the analysis comprises performing calculations at aplurality of spaced locations along the structural beam.
 4. A methodaccording to claim 3 wherein the spaced locations comprise sectionsthrough the structural beam.
 5. A method according to claim 3 or claim 4wherein the spaced locations are equidistant along the length of saidstructural beam.
 6. A method according to claim 1 wherein the structuralbeam comprises a plurality of apertures and the step of obtaining aplurality of values for a plurality of physical parameters of thestructural beam comprises obtaining aperture information comprising thelocation and size of each aperture.
 7. A method according to claim 1wherein the modifying factor information comprises a plurality ofmodifying factors at a plurality of locations and performing an analysisincludes multiplying the temperature information by the modifying factorinformation.
 8. A method according to claim 7 wherein the plurality ofmodifying factors are in the range 1.05 to 1.5.
 9. A method according toclaim 7 wherein the temperature information comprises empiricaltemperature information derived from heating the first fabricated beamcomprising a beam having a plain web and wherein the modifying factorinformation comprises empirical temperature information derived fromheating the second fabricated beam having a web provided with one ormore apertures.
 10. A method according to claim 6 wherein the analysisfurther comprises performing additional calculations in the vicinity ofthe aperture.
 11. A method according to claim 10 wherein the additionalcalculations comprise calculating one or more of; the shear resistanceof the structural beam, the bending resistance of the structural beam,Vierendeel bending resistance, web buckling.
 12. A method according toclaim 1 further comprising calculating the required thickness ofintumescent coating to avoid failure of the structural beam at aselected period of time.
 13. A method according to claim 12 furthercomprising identifying a failure mode of the structural beam andcalculating the thickness of intumescent coating required to avoid thefailure mode.
 14. A method according to claim 13 further comprisingidentifying the location where said failure mode occurs and calculatingthe required thickness at that location.
 15. A method according to claim12 comprising calculating the required thickness of intumescent coatingfor a plain beam and then performing the additional calculations inaccordance with the required thickness.
 16. A method according to claim1 wherein the output comprises comparing one or more values of said oneor more properties with a predetermined criterion and generating anoutput accordingly.
 17. A method according to claim 1 comprisingperforming said analysis for the structural beam in the cold condition.18. A method according to claim 1 comprising modifying the values for aplurality of physical parameters of the structural beam in accordancewith the output and performing the method in accordance with themodified values.
 19. A method according to claim 1, further comprisingforming a fire resistant structural beam pursuant to that design.
 20. Amethod according to claim 9 or 14, wherein the temperature informationalso comprises a plurality of temperatures at a plurality of locations,and where the temperature information for a position disposed betweentwo or more said locations is calculated by interpolating thetemperature at the two or more locations.
 21. A method according toclaim 6 wherein the analysis further comprises performing additionalcalculations in the vicinity of the aperture.
 22. A method according toclaim 1, wherein the temperature information comprises modifying factorinformation.
 23. A method according to claim 22, wherein performing ananalysis comprises calculating a strength of the structural beam at atemperature calculated using the modifying information.
 24. A methodaccording to claim 1, wherein generating an output comprises indicatingwhether the beam is likely to fail.
 25. A system for providing a methodof designing a fire resistant structural beam including a plurality ofapertures based on empirical temperature information obtained fromconducting fire tests on a first fabricated beam and a second fabricatedbeam, the system comprising: a memory that stores computer-executableinstructions in a tangible form; and a processor being adapted to theexecute the computer-executable instructions, the computer-executableinstructions comprising instructions for: obtaining a plurality ofvalues for a plurality of physical parameters of the fire resistantstructural beam; selecting a fire resistance time for the fire resistantstructural beam from a plurality of available fire resistance times;reading temperature information associated with the selected fireresistance time, the temperature information comprising, or derivedfrom, a plurality of temperatures measured at a plurality of locationson a first fabricated beam that is similar to the fire resistantstructural beam and wherein the plurality of temperatures were obtainedfrom a fire test of the first fabricated beam and measured after a timeequal to the fire resistance time had elapsed, reading modifying factorinformation associated with the selected fire resistance time, themodifying factor information comprising at least one modifying factorfor each aperture, wherein the modifying factor is derived fromempirically obtained temperatures measured adjacent an aperture of asecond fabricated beam that has undergone a fire test, performing ananalysis step comprising: calculating a first property of the fireresistant structural beam at one or more locations on the fire resistantstructural beam, the first property at each location calculated as afunction of one of the plurality of temperatures of the temperatureinformation, and calculating a second property of the fire resistantstructural beam at a plurality of locations around the apertures and onthe fire resistant structural beam, the second property at each locationaround the apertures calculated as a function of one of a plurality oftemperatures obtained by multiplying the plurality of temperatures ofthe temperature information by the modifying factor, and generating anoutput indicating whether the fire resistant structural beam is likelyto fail in accordance with the analysis step.